If they did something like this then it would be a great ongoing MP alternative that would likely sit next to Warzone and they could easily apply microtransactions through this model as they already do with Mobile and Online. I just don't know why they keep making a game from scratch every year especially when they never get better and are always riddled with balancing issues.
I tried COD Online a few years ago and it was great because you could play with MW2's weapons on Black Ops 1 maps for instance. I even got an AC-130 on Nuketown in one match! There were so many weapons in the game and you never knew what map would pop up - you could play on a WAW map one minute, COD 4 the next and then a MW3 one. If Activision commissioned a game called 'The Call of Duty' or something and made available 50 maps and 500 weapons from all the big games and just let people get on with it, it would be a huge success and players would remain engaged rather than departing or having to play the old games as a standalone and then not spending money. Something like this could be good for 3+ years and as you said above, it could run like Siege and Overwatch.
Many players are flocking third party clients on PC like IW4X for COD4 and MW2 along with Plutonium MW3 and BO2 which look great fun. Not only are those heavily supported by the creators but they also have a solid anti-cheat and content that even improves the old games such as custom maps.